Revealing mistake: During Lecter's escape, the SWAT team arrives and jumps out of the police car at the courthouse with their Ithaca 37 shotguns. All of them are shown chambering their rounds except the the officer on the right, who pulls back again on the fore stock and asks "ready?" That should've ejected a shell and left the gun unloaded. (01:21:40)
Continuity mistake: When Lecter is in the ambulance, wearing another man's face, as the ambulance officer has his back to Lecter, Lecter takes the large dressing off his face and pulls the oxygen mask down, then sits up, but when he does, the oxygen mask would be in the way; it is around his neck, he would have had to pull it over his head to get rid of it, but he didn't do this - the oxygen mask vanishes. (01:25:05)
Deliberate mistake: The number of acts Lecter performed during his escape from the individual jail cell and until he was attended to by an officer (who thought he was an injured officer) would have taken a lot of time and effort to complete - way more time than he could have gone undetected by one of the many officers in the building. Slashing/ bludgeoning to death a person can be done fairly quickly (munching on a victim's face adds time!), but three particular acts required a substantial amount of time, especially for an elderly man whose ultimate goal was escape: Swapping clothes (undressing and dressing) with a police officer and trimming off his face/scalp to appear to be that officer, then getting to a strategic location to be discovered; Setting a dead officer on the roof of the elevator; and, somehow hanging / impaling (crucifixion-style) an officer from the top of the jail cell (which appeared to be around 10' high). The latter feat would be challenging for TWO physically-fit officers.
Character mistake: Clarice was given clear, explicit instructions by Crawford before going to the asylum to see Lecter, including: do not touch the glass; do not approach the glass; tell him nothing personal; do not accept anything from him. Barney also gave the specific rules to Clarice when she got there (e.g, "you don't get near the glass"; use the food tray carrier to give him papers), and informed her he would be watching her on video. An FBI Agent TRAINEE is under close scrutiny and failure to meet the high standards and/or rigorous training can/will result in dismissal from the academy; a student must follow the rules and demonstrate she has what it takes to graduate and is suitable to become a member of the FBI. Given the high standards and relative difficulty in securing a position with the FBI, a trainee would not blatantly break the rules or virtually disregard the direct orders of a supervisor like Clarice did - especially during the very first assignment. The end does not justify the means.
Continuity mistake: When Lecter is in the Memphis jail cell, trying to escape, there is a shot of him eating the face of Sgt. Pembry, and a nano-second later, you see Lecter trying to completely shove the jail door on him. No way these two events could have transpired so quickly. (01:15:50)
Factual error: When Starling leaves from Memphis, the jet shown taking off is in St Louis, not Memphis. This can be noted by not just the McDonnell Douglas sign, but the fact that the sign is on their Headquarters Hangar, which is in St. Louis. I have lived in St louis all my life: there is no mistaking this sign and building (even in the dark) for another hangar or sign in another city. It also helps to know McDonnell Douglas had no hangar in Memphis, nor any buildings with any signage at the time of the movie at all.
Character mistake: When the scientists cut open the cocoon found in the throat of a murder victim, they are not wearing gloves even though Clarice specifically states that it was found behind the soft palate of a murder victim. (00:48:00)
Plot hole: When Clarice visits Lecter in his new makeshift cell, she brings his drawings, which were left behind in Baltimore. She tells him how she saw the lambs being killed and heard them screaming, taking one lamb with her when she ran away. As the guards approached his cell after she leaves, the camera pans across the cell, taking in the drawings Clarice had brought, and the top one is a very detailed drawing of Clarice holding a spring lamb. She only told just told Lecter about the lamb, not enough time for him to have done that drawing.
Continuity mistake: When Lecter is about to kill the two cops guarding him, he kicks the cell door preventing one of the cops from entering the cell. Just a moment later he is in front of the guard and there is no metal door in between them.
Revealing mistake: When Clarice goes to Crawford's office, on the board there is a newspaper article titled "Bill Attacks Again, Woman Missing..." on the left and another titled "FBI Links 'Skinning..." on the right. The three top paragraphs on the left columns of both are identical (with different spacing). Two of the yellow lines on the right one are the same too.
Continuity mistake: Before Clarice chases Buffalo Bill down the basement steps, she quickly slips off her green overcoat, letting it fall to the floor. (I wasn't able to see if the green/red checked blazer and/or the grey scarf she almost always wore were slipped off at the same time - the view was obstructed by a table.) After Bill is killed, Clarice exits the house and comes down the front steps wearing the green/red checked suit jacket (blazer), but does not have the green overcoat or scarf with her. (01:43:13 - 01:50:17)
Continuity mistake: On ground floor in Memphis, the female police officer says "No, nobody went up." Sgt. Tate at this point starts to croak something, and behind him as shots as heard one of the men behind him is walking forward. The feet of that person are in the circular section of the floor decoration, but in the next shot both policemen coming from that direction are a couple steps behind that spot. (01:18:50)
Continuity mistake: The two guards approach Hannibal's cage and put down the tray with the lamb dinner. Lt. Boyle murmurs "Wonder what he wants for breakfast." He is passing the club to Sgt. Pembry holding it with his right hand on the tip. In the next shot, when he finishes quipping "Some damn thing from the zoo?" his hand is on the opposite end of the baton, past the handle. (01:15:10)
Continuity mistake: Clarice is at the desk of the Courthouse in Memphis. She hands the ID to the agent, who holds it with both hands. Cut, and he's holding it with just the right hand. The female agent next to him in the second shot is leaning against her own left hand, but she had both on the desk in the first shot. (01:05:30)